About British food, is it true shortbread is Scottish, scones are Scottish, and black tea is never drunk without milk?

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Shortbread is Scottish, but the origin of scones is debatable. It could be argued the current type of scones eaten in the UK originated from Scotland, but scone-like baked goods were also common long ago on the European continent. Maybe it spread from Scotland to the mainland or the other way. We have no way to definitively know which.

There are many kinds of tea that uses black tea leaves. And there is no requirement to drink it with milk or cream. Just as there is no requirement that you must add sugar.  The custom of using milk or cream actually stemmed from a practical reason: when Europeans started to make their own porcelain wares they did not quite learned how to make them in as high a quality as the ones made in China.  Low quality porcelain wares like tea cups can crack if you pour too hot a liquid into them. So it was a common practice to pour milk/cream into the tea cup, then pour the hot tea into it.  The milk/cream keeps the temperature from being too high. 

Yes Shortbread is Scottish, Black Tea origin in East Asia, Scotland all of United Kingdom has Scottish Tea, English Breakfast Tea and has similar teas to them some are taken with milk some of them do take tea's without milk depends on their choice.

Well, there is Scottish shortbread, Scones are made all over the UK, and black tea is drunk with or without milk its just preference.

Yes, shortbread is Scottish. Scones are connected traditionally with England, Scotland, and Ireland, but nobody knows which country invented it, and no one can "prove" it is Scottish only. Black tea, like anything else, is drunk the way you like it.